Question

plzz answer it it is veryburgent ... 50 POINTS QUESTION...​

Answer 1

Answer:

1/8

Step-by-step explanation:

cos 5π/8=cos(π/2 + π/8) = -sin π/8

cos 3π/8=cos(π/2 - π/8) = sin π/8

cos 7π/8=cos(π - π/8) = -cos π/8.

Given,

(1 + cos π/8)(1 + cos 3π/8)(1 + cos 5π/8)(1 + cos 7π/8)

⇒ (1 + cos π/8)(1 + sin π/8)(1 - sin π/8)(1 - cos π/8)

⇒ [1 - (cos π/8)²][1 - (sin π/8)²]

⇒ (sin π/8)² * (cos π/8)²

⇒ 1/4 * (2 sin π/8 * cos π/8)²

[∵ 2 sin ∅ cos ∅ = sin 2∅]

⇒ 1/4(sin 2 *  π/8)²

⇒ 1/4(sin π/4)²

⇒ 1/4 * 1/2

⇒ 1/8

Hope it helps!

Answer 2

hi mate,

solution :

cos 5π/8=cos(π/2 + π/8) = -sin π/8

cos 3π/8=cos(π/2 - π/8) = sin π/8

cos 7π/8=cos(π - π/8) = -cos π/8.

Given,

(1 + cos π/8)(1 + cos 3π/8)(1 + cos 5π/8)(1 + cos 7π/8)

= (1 + cos π/8)(1 + sin π/8)(1 - sin π/8)(1 - cos π/8)

= [1 - (cos π/8)²][1 - (sin π/8)²]

= (sin π/8)² * (cos π/8)²

= 1/4 * (2 sin π/8 * cos π/8)²

(∵ 2 sin ∅ cos ∅ = sin 2∅ )

= 1/4(sin 2 *  π/8)²

= 1/4(sin π/4)²

= 1/4 * 1/2

= 1/8

I hope it helps you.